Dried shitakes, for sure. Or if you're looking for woodsy depth, dried porcini. Doesn't take much. Any kind of bean you otherwise don't often have. Fageole or white beans can be muy satisfying. Rosemary. A little farro or barley to add body to brothy dishes…

I have some dried shitakes left over from hot and sour. Do you just throw them in dried? I can't remember if I had to wash these last time. Definitely going with white beans and something deep. What's the classic white bean stew? I can't remember. A smoked pork knuckle goes a long way.

It doesn't hurt to give them a quick rinse, but the hydration will depend on having a enough broth/water in your concoction, and enough time. I'm guessing your cooking cycle will provide plenty of time.

If you eat meat, you might look to recipes for cassoulet for inspiration. With that dish, it's all about slow-cooking.